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Claim. Write $f^{(3)}(n;s,j)$ for the largest number of edges of a $3$-uniform hypergraph on $n$ vertices containing no $j$ edges on at most $s$ vertices, and $\pi(j)$ for the limit of $n^{-2}f^{(3)}(n;j+2,j)$, which exists by Delcourt and Postle; this is the paper's notation with its $k$, the number of edges, written $j$ here to keep erdosproblems.com's $k$. Theorem 1.1 of Bodnár, Pikhurko, Sun, Wang and Zeng states that $\pi(9)=1/5$. The $3$-graphs with no nine edges on at most eleven vertices are exactly the $3$-graphs with no member of erdosproblems.com's $\mathcal F_{11}$, the family with $11$ vertices and $9$ edges, so

$$\mathrm{ex}_3(n,\mathcal F_{11})=\Bigl(\frac15+o(1)\Bigr)n^2,$$

not $(1+o(1))n^2/6$: the displayed asymptotic fails at $k=11$ with $\mathcal F_k$ the single family the erdosproblems.com wording defines, so the erdosproblems.com wording, an assertion about every $k\ge5$, is false. The transfer from the theorem to the erdosproblems.com wording is the identification of the two forbidden families.

The refutation needs only the lower bound $\pi(9)\ge1/5$, which Section 3 of the paper proves by a finite-field construction: a $3$-graph built from blocks of diamonds sharing a private pair, in which every $h$ edges span at least $h+2$ vertices for $3\le h\le8$ and every nine edges span at least twelve (Lemma 3.3), fed to the packing theorem of Glock, Joos, Kim, Kühn, Lichev and Pikhurko (the paper's Theorem 3.1). The matching upper bound comes from linear programs that a computer generates and solves, with the code and certificates in the arXiv ancillary folder. The paper's declaration of generative AI use (p. 13) says that the authors used ChatGPT to help with the finite case analysis behind the construction, including a Python program it generated for the vertex counts in the proof of Lemma 3.3, and that generative AI wrote some routine parts of the SageMath code for the upper bound. The paper says the result was obtained independently of Chao, Huang and Liu, whose Theorem 1.1 contains it. Its Theorem 1.2, $\pi(8)\le5053/26544$, is an upper bound at $k=10$ and refutes nothing; with the lower bound $3/16$ on the (10,8) page it places the limit at $k=10$ between $3/16=0.1875$ and $5053/26544\approx0.19036$.

Why it is rejected. It answers the erdosproblems.com wording, the single family $\mathcal F_{11}$, not the modified Statement of Problem 1076, whose family is cumulative: under the modified Statement a $3$-graph avoiding $\mathcal F_4\cup\dots\cup\mathcal F_{11}$ is linear, so the theorem says nothing against it, and the page does not count toward the problem's standing. The problem page's Notes credit the result.

Acceptance. None documented. The paper is an arXiv preprint, read in its first version (2 October 2026): the abstract, the introduction with Theorems 1.1 and 1.2 (pp. 1--3), the lower-bound proof of Section 3 and the declaration of generative AI use (p. 13). erdosproblems.com does not cite it on this problem, and its curator makes no statement about it. The proof is unreviewed, the computer certificates were not run here, and no formalization is known.